From 90e27b580346283dc372ad5d4b2cb48d5bf14b6d Mon Sep 17 00:00:00 2001
From: bjorn-stevens <64255981+bjorn-stevens@users.noreply.github.com>
Date: Fri, 12 Aug 2022 14:43:58 +0200
Subject: [PATCH] added new formulats for saturation vapor pressure
the murphy and koop (2005) and hardy (1998) formulations for
saturation vapor pressure are sometimes desired. The former
for their ability to handle saturation over supercooled liquid,
the latter because this equation is frequenly used for the
processing of radio sonde data
---
moist_thermodynamics/functions.py | 41 +++++++++++++++++++++++++++++++
1 file changed, 41 insertions(+)
diff --git a/moist_thermodynamics/functions.py b/moist_thermodynamics/functions.py
index e9813d8..e0c0f42 100644
--- a/moist_thermodynamics/functions.py
+++ b/moist_thermodynamics/functions.py
@@ -105,6 +105,47 @@ def es_mxd(T):
"""
return np.minimum(es_liq(T),es_ice(T))
+def es_liq_murphykoop(T):
+ """Returns saturation vapor pressure (Pa) over liquid water
+
+ Encodes the empirical fit (Eq. 10) of Murphy and Koop (2011) which improves on the Wagner and
+ Pruß fits for supercooled conditions.
+
+ Args:
+ T: temperature in kelvin
+
+ Reference:
+ Murphy, D. M. & Koop, T. Review of the vapour pressures of ice and supercooled water for
+ atmospheric applications. Q. J. R. Meteorol. Soc. 131, 1539–1565 (2005).
+
+ >>> es_liq_murphykoop(np.asarray([273.16,140.]))
+ array([6.11657044e+02, 9.39696372e-07])
+ """
+
+ X = np.tanh(0.0415*(T - 218.8)) * (53.878 - 1331.22/T - 9.44523 * np.log(T) + 0.014025*T)
+ return np.exp(54.842763 - 6763.22/T - 4.210*np.log(T) + 0.000367*T + X)
+
+def es_liq_hardy(T):
+ """Returns satruation vapor pressure (Pa) over liquid water
+
+ Encodes the empirical fit (Eq. 10) of Hardy (1998) which is often used in the postprocessing
+ of radiosondes
+
+ Args:
+ T: temperature in kelvin
+
+ Reference:
+ Hardy, B., 1998, ITS-90 Formulations for Vapor Pressure, Frostpoint Temperature, Dewpoint
+ Temperature, and Enhancement Factors in the Range –100 to +100 °C, The Proceedings of the
+ Third International Symposium on Humidity & Moisture, London, England
+
+ >>> es_liq_hardy(np.asarray([273.16,260.]))
+ array([611.65715494, 222.65143353])
+ """
+ X = (-2.8365744e+3/(T*T) - 6.028076559e+3/T + 19.54263612 - 2.737830188e-2*T
+ + 1.6261698e-5*T**2 + 7.0229056e-10*T**3 - 1.8680009e-13*T**4 + 2.7150305 * np.log(T))
+ return np.exp(X)
+
def es_liq_analytic(T, delta_cl=constants.delta_cl):
"""Analytic approximation for saturation vapor pressure over iquid
--
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